Resolution Dependence in Magnetohydrodynamic Simulations of Neutrino-Driven Core-Collapse Supernovae

TL;DR

The paper investigates how numerical resolution and initial magnetic field strength influence neutrino-driven core-collapse supernovae in 3D MHD simulations of a non-rotating $13\,M_\odot$ progenitor using CoCoNuT-FMT. Six models spanning four grid resolutions and two field strengths reveal that shock revival timing is robust, but higher resolution and stronger magnetisation yield larger explosion energies via amplified magnetic energy in the gain region and PNS, driven by a small-scale dynamo. Neutrino luminosities and mean energies tend to decrease with increasing resolution due to PNS distortion from stronger fields, while magnetic energy growth enhances energy transport behind the shock. Strong magnetic fields can lead to magnetar-strength remnants and substantial PNS spin-up, highlighting the significant role of MHD effects in late-time supernova evolution and the need for longer, multi-code resolution studies to quantify uncertainties.

Abstract

We investigate the role of resolution and initial magnetic field strength on core-collapse supernovae in simulations of a non-rotating $13 \mathrm{M_\odot}$ progenitor. Specifically, we study the effect on shock revival, explosion dynamics, and the properties of the compact remnant. We run four models with different numerical grid resolutions with an initial central dipole field strength of $\mathord{\approx}10^{12}\, \mathrm{G}$. Two of those resolutions are also run with a weaker central magnetic field of $\mathord{\approx}10^{10}\, \mathrm{G}$ . The shock revival time for all models is largely independent of resolution and initial magnetic field strength, but we find higher explosion energies when the initial magnetism is stronger and at higher resolutions. We find that models with strong magnetic fields have lower neutrino luminosity and energies, due to a proto-neutron star (PNS) that is deformed by the strong magnetic fields. At higher resolutions, magnetic fields are amplified more efficiently in the gain region and in the PNS via the small-scale dynamo. Although the strong magnetic fields do not directly drive the explosion, they have a subsidiary impact on the explosion mechanism and compensate for the reduced neutrino heating. Stronger magnetic energies in the PNS also affect energy and angular momentum redistribution, leading to more extended and vigorous PNS convection zones at higher resolutions.

Figures (15)

• Figure 1: Initial density (red) and entropy (black) profiles mapped from MESA to CoCoNuT-FMT.
• Figure 2: The evolution of the mean shock radius (left) and diagnostic explosion energy (right) for the entire set of simulations.
• Figure 3: Entropy (left) and root mean squared magnetic field strength (right) for models LRes, MRes and HRes (from top to bottom) models at 0.17 s post-bounce up to a radius of 300 km. The entropy colourbars are in units $\mathrm{k_b/baryon}$, and the decadic logarithm of the magnetic field strength in $G$ is plotted from $10^9$ - $10^{15}$ G
• Figure 4: Hydrodynamic enthalpy flux ($F_\mathrm{h}$, dashed) and total energy flux ($F_\mathrm{t}$, solid) at 0.20 s post-bounce up to 1000 km. The vertical dashed line gives the approximate radius ($\approx$100 km) above which the angle-averaged total energy in the outflows becomes positive.
• Figure 5: Neutrino luminosity (left) and neutrino mean energy (right) for electron neutrinos, $\nu_\mathrm{e}$ (top), electron antineutrinos, $\bar{\nu}_\mathrm{e}$(middle), and heavy-flavour neutrinos, $\nu_x$(bottom), respectively.